Entropy and chirality in sphinx tilings
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910351641018368 |
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| author | Huber, Greg Knecht, Craig Trump, Walter Ziff, Robert M. |
| author_facet | Huber, Greg Knecht, Craig Trump, Walter Ziff, Robert M. |
| contents | As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor ("Sphinx frames") require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using "accelerated backtracking," "seam," and "dangler" algorithms. For larger frames, we introduce a Monte Carlo (MC) method to sample typical tilings. Key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropy and chirality in sphinx tilings Huber, Greg Knecht, Craig Trump, Walter Ziff, Robert M. Statistical Mechanics Disordered Systems and Neural Networks As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor ("Sphinx frames") require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using "accelerated backtracking," "seam," and "dangler" algorithms. For larger frames, we introduce a Monte Carlo (MC) method to sample typical tilings. Key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation. |
| title | Entropy and chirality in sphinx tilings |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2304.14388 |